def is_increasing(a):
    return all(a[i]<=a[i+1] for i in range(len(a)-1))

def do_swaps(a,b,swaps):
    return (tuple(b[i] if swaps[i] else a[i] for i in range(len(a))),
            tuple(a[i] if swaps[i] else b[i] for i in range(len(a))))


def is_solvable(a,b):
    n = len(a)
    return any(all(is_increasing(x) for x in pair) for pair in [do_swaps(a,b,swaps) for swaps in cartesian_product([[0,1]]*n)])


def f(n,k):
    X = cartesian_product([range(k)]*n)
    return sum(1 for a,b in cartesian_product([X, X]) if is_solvable(a,b))


def get_graph(n,k):
    X = cartesian_product([range(k)]*n)
    Y = [x for x in X if is_increasing(x)]
    g = Graph()
    g.allow_loops(True)
    for a,b in cartesian_product([X, X]):
        for swaps in cartesian_product([[0,1]]*n):
            g.add_edge((a,b), do_swaps(a,b,swaps))
    return g, [p for p in g.vertices() if all(x in Y for x in p)]


#print (is_solvable((1,0), (0,1)))
#print ([f(n,4) for n in range(1, 4)])
g, Y = get_graph(3, 3)
show(g.plot(figsize=100, vertex_colors={'green': Y}))